The present invention relates to a second order all pass network for phase compensation of signals and more particularly to a second order active all pass network suited for integration thereof into an intergrated circuit (IC).
Video signals having a wide frequency range are signal-treated through a plurality of filter circuit stages so that desired frequency characteristics are provided therefor. In such cases, it sometimes becomes necessary to copensate for phase characteristics.
FIG. 3 is a block diagram showing an example of a prior art second order all pass network which has thus far been used for phase compensation.
Referring to the drawing, reference numerals 1 and 2 denote voltage-current converting circuits formed of differential amplifiers as the fundatmental component parts thereof and 3 denotes a buffer amplifier whose gain is unity.
In such a circuit, when mutual conductances g.sub.m of the first and second voltage-current converting circuits 1 and 2 are set at 1/r.sub.2 and 1/r.sub.1, respectively, and capacitances of the capacitors C.sub.1 and C.sub.2 are set at c.sub.1 and c.sub.2, respectively, a relationship between the signal V.sub.i at the input terminal T.sub.i and the signal V.sub.0 at the output terminal T.sub.0 is given by ##EQU1## where V.sub.y is a potential at the point Y and .omega. is the angular frequency.
Eliminating V.sub.y from the above equations (1) and (2), we obtain ##EQU2##
Accordingly, .vertline.V.sub.0 /V.sub.i .vertline. becomes constant for any magnitude of the angular frequency .omega.. That is, an all pass network in which a flat gain characteristic is maintained and only the phase is changed is obtained. The phase characteristic, as shown in FIG. 4, is that of a second order all pass network, in which there is no phase lag at .omega.=0 and a lag of 360.degree. at .omega.=.infin..
If now the values of the mutual conductance (1/r.sub.1) and the capacitances c.sub.1 and c.sub.2 of the capacitors are selected to satisfy ##EQU3## then the above equation (4) is reduced to ##EQU4## This equation shows that the phase rotation becomes 180.degree. at .omega.=.omega..sub.c. The characteristic as shown in the dotted line in FIG. 4 is provided when the Q factor, which indicates the degree of the phase rotation, is high. The characteristic as shown in the one-dot chain line is provided when the Q factor is low.
In a demodulator circuit for a video signal or the like, a second order all pass network with a low Q factor of, for example, 0.5 or so is required for compensation of the group delay characteristic of a filter.
In the above described second order all pass network, if c.sub.1 is equal to c.sub.2, the Q factor becomes 1.414 because ##EQU5##
To make Q=0.5 or less, the ratio c.sub.2 /c.sub.1 must be made 8, at the lowest. However, a capacitor provided in an IC structure in general can be provided to the highest accuracy only when its capacitance is 5 to 7 PF. If it is lower than this, the effect of the error due to stray capacity becomes larger. Also, it is difficult to provide a capacitor of larger capacitance in the IC structure. If it could be made, the chip size would become larger and impracticable.
Thus, the prior art second order all pass network has the problem that its Q factor is difficult to set at a desired value when it is integrated in an IC, and more particularly the second order all pass network has a low Q factor which could not be provided in an IC structure with accuracy.